Pith Number

pith:4XBSXFEG

pith:2011:4XBSXFEGLH3CDN5ZLZZFQUPFW5

not attested not anchored not stored refs pending

Generalized covariation and extended Fukushima decompositions for Banach valued processes. Application to windows of Dirichlet processes

Cristina Di Girolami (Luiss Guido Carli), Francesco Russo (UMA)

arxiv:1105.4419 v1 · 2011-05-23 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4XBSXFEGLH3CDN5ZLZZFQUPFW5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:21:29.295623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5c32b948659f621b7b95e725851e5b751a68b19eff332c3891a8a06d6987f0e

Aliases

arxiv: 1105.4419 · arxiv_version: 1105.4419v1 · doi: 10.48550/arxiv.1105.4419 · pith_short_12: 4XBSXFEGLH3C · pith_short_16: 4XBSXFEGLH3CDN5Z · pith_short_8: 4XBSXFEG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4XBSXFEGLH3CDN5ZLZZFQUPFW5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e5c32b948659f621b7b95e725851e5b751a68b19eff332c3891a8a06d6987f0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "733c66de76ef2b0183049db1515c62f70ae6f0ac34ff410adb42b37a8cae57e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-05-23T07:33:17Z",
    "title_canon_sha256": "81a05cc7db4482e359f8084cdd93e63b5c0e4ef2c2d7701f6f0c7d0e0326d012"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4419",
    "kind": "arxiv",
    "version": 1
  }
}